If `|a_1sinx+a_2sin2x++a_nsinn x|lt=|sinx|` for `x in R ,` then prove that `|a_1+2a_1+3a+3+n a_n|lt=1`

If |a_1sinx+a_2sin2x++a_nsinn x|lt=|sinx| for x in R , then prove that |a_1+2a_2+3a_3+n a_n|lt=1

If |a_1sinx+a_2sin2x++a_nsinn x|lt=|sinx| for x in R , then prove that |a_1+2a_2+3a_3+n a_n|lt=1

If |a_1Sinx+a_(2)sin2x+.....+a_(n)sinx|le|sinx| for x in R then maimum value of |a_(1)+2a_(2)+3a_(3)+.....+na_(n)| is

Suppose p(x)=a_0+a_1x+a_2x^2+...+a_n x^ndot If |p(x)|lt=|e^(x-1)-1| for all xgeq0, prove that |a_1+2a_2+...+n a_n|lt=1.

Suppose p(x)=a_0+a_1x+a_2x^2++a_n x^ndot If |p(x)|lt=e^(x-1)-1| for all xgeq0, prove that |a_1+2a_2++n a_n|lt=1.

If a_n=sin^n theta+cosec^ntheta and a_1=2 prove that, a_n=2 .

If a_1. a_2 ....... a_n are positive and (n - 1) s = a_1 + a_2 +.....+a_n then prove that (a_1 + a_2 +....+a_n)^n ge (n^2 - n)^n (s - a_1) (s - a_2)........(s - a_n)

If f(x)=(a_1x+b_1)^2+(a_2x+b_2)^2+...+(a_n x+b_n)^2 , then prove that (a_1b_1+a_2b_2++a_n b_n)^2lt=(a1 2+a2 2++a n2)^(b1 2+b2 2++b n2)dot

If f(x)=(a_1x+b_1)^2+(a_2x+b_2)^2+...+(a_n x+b_n)^2 , then prove that (a_1b_1+a_2b_2+...+a_n b_n)^2lt=(a_1^ 2+a_2^ 2+...+a_ n^2)(b_1^ 2+b_2^ 2+..+b_ n^2)dot

If f(x)=(a_1x+b_1)^2+(a_2x+b_2)^2+...+(a_n x+b_n)^2 , then prove that (a_1b_1+a_2b_2+...+a_n b_n)^2lt=(a_1^ 2+a_2^ 2+...+a_ n^2)(b_1^ 2+b_2^ 2+..+b_ n^2)dot